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Exercise A

Avg difficulty 3.0

Show that each of the following is neither a validity nor a contradiction:

  1. D(a)∧D(b)D(a)\wedge D(b)

  2. ∃x T(x,h)\exists x\,T(x,h)

  3. P(m)∧¬∀x P(x)P(m)\wedge\neg\forall x\,P(x)

  4. ∀z J(z)↔∃y J(y)\forall z\,J(z)\leftrightarrow\exists y\,J(y)

  5. ∀x(W(x,m,n)∨∃y L(x,y))\forall x(W(x,m,n)\vee\exists y\,L(x,y))

  6. ∃x(G(x)→∀y M(y))\exists x(G(x)\rightarrow\forall y\,M(y))

  7. ∃x(x=h∧x=i)\exists x(x=h\wedge x=i)

Magnus et al., forall x: Calgary, Interpretations, Using interpretations, Exercise A

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Adapted from forall x: Calgary © 2025 P. D. Magnus, Tim Button, Robert Trueman, and Richard Zach. Licensed under CC BY 4.0. Source: forall x: Calgary. Imported at revision ec34df8.